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M.Tech / M.E / PhD Thesis | Mathematics | India | Volume 6 Issue 8, August 2017

# Bianchi Type V String Having G and Λ as a Constant in a Cosmological Model

**Abstract: **In view of universe Bianchi Type V and Gravitational constant G and Cosmological constant play an important role for the study of entire universe. Due to the special cases it becomes more interesting because it contains special characters and permits arbitrary small an isotropic levels time to time. At the very every stage of the formation of universe the string theory place a very important role as a study in physical situation. After Big Bang theory it was assume that the universe goes under several critical changes as its temperature goes down which is predicted by grand unified theories. It is highly believed that the universe is broken spontaneously during its phase transactions during its early stages. The walls strings and monopoles arise because of topological stable defects. In the above all three interplanetary strings are most exciting as it is believe that it give rise to density perturbations which gives the formation of different galaxies. The above said cosmic strings are in the form of closed loops or may be open like air. So, that they moved through period and we can trace them out like sheet or spout. As the cosmic string, is open to shudder and it will produce distinct vibration ways, which contains Gravitational force due to the presence of small particles. Hence it is very interesting to study the Einstein field equation for Gravitational effect formed by these strings. Bianchi cosmology is the study of universes. In cosmology we are mainly interested in three-dimensional spatial sections. The Bianchi models are cosmological models that have spatially homogeneous sections, invariant under the action of a three-dimensional Lie group. The classification of the three-dimensional Lie algebra is called the Bianchi classification, and each Lie algebra is labeled by a number I-IX. By using one of these Lie algebras, we can construct a spatially homogeneous cosmological model. The corresponding cosmological model is called a Bianchi model. If a Bianchi model has the symmetry from the type III algebra, say, we say that it is a Bianchi type III model. Standard cosmological models assume that the universe, on cosmological scales, is both homogeneous (looks the same at every place) and isotropic (looks the same in every direction). If the assumption is relaxed, so that the further condition holds but not the latter, then the allowed solutions of the equations of general relativity are called Bianchi models. Related to the stars and the universe constant mostly (event (s) or object (s) that prove something) Lambda is asked/encouraged by Albert Einstein as a (changing to one form, state, or state of mind to another) of his original explanation of general relativity to (accomplish or gain with effort) an unmoving universe. To obtain the general solution Letelier and Stachel gives the overall relativistic treatment for the string by using field equation of Einstein for a cloud contains different symmetrical shapes for strings. In Bianchi Type-I gigantic string cosmological model is obtained by Litelier, Banerjee has studied Bianchi Type-I string dust may or may not having magnetic field. The same solution for different Bianchi Types i. e. (II, VI_0, VIII, IX) all was studied by Krori and Wang. The dust magnetized cosmological model was presented in LRS Bianchi Type-I by Bali & Upadhaya with G_3symmetry. Singh & Singh studied the cosmological model with magnetic field in Bianchi type studied by Krori. The Bianchi cosmologies play an important role in theoretical cosmology and have been much studied since the 1960s. Bianchi cosmological models are spatially homogeneous space time. A spatially homogeneous Bianchi model necessarily has a three dimensional group, which acts simply transitivity on space-like three dimensional orbits. For simplification and description of the large scale behavior of the actual universe, locally rationally symmetric Bianchi type I space time have widely studied. When the Bianchi type I space time expands equally in two spatial directions it is called locally rotationally symmetric. Here we confine ourselves to a LRS model of Bianchi type I. The metric of this model is given by ds^2=dt^2-A^2 dx^2-B^2 (dy^2+dz^2) Where A and B are functions of cosmic time tonly. The Einstein field equations (EFE) are a set of ten equations in Albert Einsteins general explanation of relativity which describe the basics communication of gravitation as a happen of space-time being twisty by matter and fire. First published by Einstein in 1915 as a tens or equation, the EFE equate space-time curvature with the energy and thrust within that (something that continues from one extreme to the other). The solutions of the EFE are the parts/pieces of the measured tensor. The earliest arc-like paths of grain and radiation in resulting geometry are then guessed (a number) using the (shaped like a soccer ball) equation. These In Bianchi Type- V negative curvature FRW model

**Keywords:** Cosmological Principal, Cosmological Constant, String, Einstein Field Equation

**Edition:** Volume 6 Issue 8, August 2017,

**Pages:** 1453 - 1457